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Properties

Label 435.4.a
Level $435$
Weight $4$
Character orbit 435.a
Rep. character $\chi_{435}(1,\cdot)$
Character field $\Q$
Dimension $56$
Newform subspaces $12$
Sturm bound $240$
Trace bound $2$

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Defining parameters

Level: \( N \) \(=\) \( 435 = 3 \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 435.a (trivial)
Character field: \(\Q\)
Newform subspaces: \( 12 \)
Sturm bound: \(240\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_0(435))\).

Total New Old
Modular forms 184 56 128
Cusp forms 176 56 120
Eisenstein series 8 0 8

The following table gives the dimensions of the cuspidal new subspaces with specified eigenvalues for the Atkin-Lehner operators and the Fricke involution.

\(3\)\(5\)\(29\)FrickeDim
\(+\)\(+\)\(+\)\(+\)\(5\)
\(+\)\(+\)\(-\)\(-\)\(8\)
\(+\)\(-\)\(+\)\(-\)\(6\)
\(+\)\(-\)\(-\)\(+\)\(9\)
\(-\)\(+\)\(+\)\(-\)\(7\)
\(-\)\(+\)\(-\)\(+\)\(8\)
\(-\)\(-\)\(+\)\(+\)\(10\)
\(-\)\(-\)\(-\)\(-\)\(3\)
Plus space\(+\)\(32\)
Minus space\(-\)\(24\)

Trace form

\( 56 q + 212 q^{4} + 12 q^{6} + 64 q^{7} + 504 q^{9} + O(q^{10}) \) \( 56 q + 212 q^{4} + 12 q^{6} + 64 q^{7} + 504 q^{9} + 20 q^{10} - 136 q^{11} + 48 q^{12} - 88 q^{13} - 192 q^{14} - 60 q^{15} + 820 q^{16} + 64 q^{17} + 368 q^{19} + 80 q^{20} + 264 q^{21} - 252 q^{22} + 208 q^{23} + 144 q^{24} + 1400 q^{25} + 672 q^{26} + 700 q^{28} + 728 q^{31} - 1240 q^{32} + 148 q^{34} + 520 q^{35} + 1908 q^{36} + 320 q^{37} - 1064 q^{38} + 336 q^{39} - 60 q^{40} - 968 q^{41} + 468 q^{42} - 848 q^{43} - 520 q^{44} + 1128 q^{46} - 1168 q^{47} + 576 q^{48} + 984 q^{49} + 408 q^{51} + 1444 q^{52} + 1072 q^{53} + 108 q^{54} - 1120 q^{55} + 336 q^{56} - 168 q^{57} - 232 q^{58} - 1024 q^{59} + 180 q^{60} + 600 q^{61} - 328 q^{62} + 576 q^{63} + 1824 q^{64} + 520 q^{65} + 2472 q^{67} - 1040 q^{68} - 432 q^{69} + 1920 q^{70} - 1072 q^{71} + 1016 q^{73} + 808 q^{74} + 5320 q^{76} - 3776 q^{77} + 1764 q^{78} + 2264 q^{79} + 640 q^{80} + 4536 q^{81} - 5408 q^{82} + 1080 q^{83} - 816 q^{84} - 440 q^{85} + 3344 q^{86} - 1044 q^{87} + 440 q^{88} - 104 q^{89} + 180 q^{90} + 1528 q^{91} - 1832 q^{92} + 2856 q^{93} - 6396 q^{94} + 80 q^{95} + 804 q^{96} + 328 q^{97} - 8200 q^{98} - 1224 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_0(435))\) into newform subspaces

Label Char Prim Dim $A$ Field CM Minimal twist Traces A-L signs Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$ 3 5 29
435.4.a.a 435.a 1.a $1$ $25.666$ \(\Q\) None 435.4.a.a \(-2\) \(-3\) \(5\) \(29\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-2q^{2}-3q^{3}-4q^{4}+5q^{5}+6q^{6}+\cdots\)
435.4.a.b 435.a 1.a $1$ $25.666$ \(\Q\) None 435.4.a.b \(-1\) \(3\) \(5\) \(4\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-q^{2}+3q^{3}-7q^{4}+5q^{5}-3q^{6}+\cdots\)
435.4.a.c 435.a 1.a $1$ $25.666$ \(\Q\) None 435.4.a.c \(5\) \(-3\) \(5\) \(16\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q+5q^{2}-3q^{3}+17q^{4}+5q^{5}-15q^{6}+\cdots\)
435.4.a.d 435.a 1.a $2$ $25.666$ \(\Q(\sqrt{41}) \) None 435.4.a.d \(-1\) \(6\) \(10\) \(-13\) $-$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta q^{2}+3q^{3}+(2+\beta )q^{4}+5q^{5}-3\beta q^{6}+\cdots\)
435.4.a.e 435.a 1.a $2$ $25.666$ \(\Q(\sqrt{34}) \) None 435.4.a.e \(0\) \(6\) \(-10\) \(0\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+3q^{3}-8q^{4}-5q^{5}+\beta q^{7}+9q^{9}+\cdots\)
435.4.a.f 435.a 1.a $5$ $25.666$ \(\mathbb{Q}[x]/(x^{5} - \cdots)\) None 435.4.a.f \(2\) \(-15\) \(-25\) \(-29\) $+$ $+$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}-3q^{3}+(2+\beta _{2})q^{4}-5q^{5}+\cdots\)
435.4.a.g 435.a 1.a $6$ $25.666$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 435.4.a.g \(-1\) \(-18\) \(30\) \(23\) $+$ $-$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(2+\beta _{1}+\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
435.4.a.h 435.a 1.a $6$ $25.666$ \(\mathbb{Q}[x]/(x^{6} - \cdots)\) None 435.4.a.h \(1\) \(18\) \(-30\) \(47\) $-$ $+$ $-$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(8+\beta _{1}+\beta _{2})q^{4}+\cdots\)
435.4.a.i 435.a 1.a $7$ $25.666$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 435.4.a.i \(-2\) \(-21\) \(35\) \(-50\) $+$ $-$ $-$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}-3q^{3}+(3+\beta _{1}+\beta _{2})q^{4}+\cdots\)
435.4.a.j 435.a 1.a $7$ $25.666$ \(\mathbb{Q}[x]/(x^{7} - \cdots)\) None 435.4.a.j \(-1\) \(21\) \(-35\) \(-37\) $-$ $+$ $+$ $\mathrm{SU}(2)$ \(q-\beta _{1}q^{2}+3q^{3}+(2+\beta _{1}+\beta _{2})q^{4}+\cdots\)
435.4.a.k 435.a 1.a $8$ $25.666$ \(\mathbb{Q}[x]/(x^{8} - \cdots)\) None 435.4.a.k \(-4\) \(-24\) \(-40\) \(-1\) $+$ $+$ $-$ $\mathrm{SU}(2)$ \(q+(-1+\beta _{1})q^{2}-3q^{3}+(5+\beta _{2})q^{4}+\cdots\)
435.4.a.l 435.a 1.a $10$ $25.666$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None 435.4.a.l \(4\) \(30\) \(50\) \(75\) $-$ $-$ $+$ $\mathrm{SU}(2)$ \(q+\beta _{1}q^{2}+3q^{3}+(7+\beta _{2})q^{4}+5q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_0(435))\) into lower level spaces

\( S_{4}^{\mathrm{old}}(\Gamma_0(435)) \simeq \) \(S_{4}^{\mathrm{new}}(\Gamma_0(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(29))\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(87))\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(\Gamma_0(145))\)\(^{\oplus 2}\)